(669d) Physics-Informed Neural Network-Based Modeling and Performance Optimization for Simulated Moving Bed Systems

Simulated Moving Bed (SMB) chromatography is an advanced, continuous separation technique widely used in chemical, pharmaceutical, and biotechnological industries for separating mixtures with high efficiency and productivity. [1-2] Unlike traditional batch chromatography, SMB mimics the counter-current movement of solid and liquid phases by periodically switching inlet and outlet ports, allowing for continuous operation and improved use of adsorbents. Solving the optimization problem—typically involving operating parameters including flow rates, switching times, and feed concentrations—is crucial to maximize key performance metrics such as product purity, recovery, and throughput. However, a key challenge in modeling SMB systems is treating the dynamics; the process does not reach a steady state but Cyclic Steady State (CSS), where the concentration profiles within the columns repeat identically from one switching period to the next. Traditional numerical methods such as the Finite Element Method (FEM) cannot impose the CSS condition directly. [2] Instead, they must simulate many switching cycles to gradually reach the CSS, resulting in high computational cost. This limitation becomes even more pronounced when these simulations are embedded in an optimization framework, where the process must be repeated for numerous candidate operating conditions.

In recent years, more and more studies have explored the use of Physics-Informed Neural Networks (PINNs) [3] for modeling complex chromatographic systems due to their ability to incorporate physical laws directly into the learning process. Our previous work [4] applied PINNs to solve the parameter estimation problem in a single-column chromatographic system. This study not only demonstrated the ability of PINNs to accurately estimate model parameters but also highlighted their significantly improved computational efficiency compared to the FEM. Tang et al. [5] addressed the optimization of a continuous capture process in the four-column periodic counter-current chromatographic system using PINNs, focusing on maximizing key performance indicators such as productivity and resin utilization. In their study, a continuous capture process is optimized over four cycles without enforcing the steady state condition. The problem of satisfying the CSS condition within the framework of PINN has yet to be addressed.

In this work, we propose and demonstrate an optimization approach utilizing the PINN technology for SMB chromatographic systems. Unlike the conventional FEM methods, the proposed PINN can directly impose the CSS condition by treating it as part of the initial conditions in the model. This allows PINNs to learn solutions that satisfy CSS without simulating multiple cycles, significantly reducing computational cost. Furthermore, the proposed PINN can handle parameter variations—it can be trained to simulate the SMB system across a wide range of design parameters within a defined space [6] to evaluate the outputs (e.g., purity and recovery). This enables efficient optimization: without the need to re-solve the model for each design point, which allows us to simply sift through the dataset to identify the optimal configuration that maximizes or minimizes the desired objective functions while satisfying constraints. This approach allows computationally efficient design of SMB systems.

[1] Kawajiri, Y., & Biegler, L. T. (2006). Optimization strategies for simulated moving bed and PowerFeed processes. AIChE Journal, 52(4), 1343-1350.

[2] Yang, Y., Chen, X., & Zhang, N. (2018). Optimizing control of adsorption separation processes based on the improved moving asymptotes algorithm. Adsorption Science & Technology, 36(9-10), 1716-1733.

[3] Subraveti, S. G., Li, Z., Prasad, V., & Rajendran, A. (2022). Can a computer “learn” nonlinear chromatography?: Physics-based deep neural networks for simulation and optimization of chromatographic processes. Journal of Chromatography A, 1672, 463037.

[4] Zou, T., Yajima, T., & Kawajiri, Y. (2024). A parameter estimation method for chromatographic separation process based on physics-informed neural network. Journal of Chromatography A, 1730, 465077.

[5] Tang, S. Y., Yuan, Y. H., Sun, Y. N., Yao, S. J., Wang, Y., & Lin, D. Q. (2024). Developing physics-informed neural networks for model predictive control of periodic counter-current chromatography. Journal of Chromatography A, 465514.

[6] PhysicsNeMo Contributors. (2023, February 24). NVIDIA PhysicsNeMo: An open-source framework for physics-based deep learning in science and engineering. https://github.com/NVIDIA/physicsnemo